What is the integral of cos(x)sqrt(x) ?

The integral of cos(x)sqrt(x) is sqrt(x)sin(x)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C

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integral of cos(x)sqrt(x)

\int cos (x) x d x

x sin (x) - \frac{π}{2} § (\frac{2}{π} x) + C

Solution steps

\int cos (x) x d x

Apply Integration By Parts

: x sin (x) - \int \frac{sin ( x )}{2 x} d x

= x sin (x) - \int \frac{sin ( x )}{2 x} d x

\int \frac{sin ( x )}{2 x} d x = \frac{π}{2} § (\frac{2}{π} x)

= x sin (x) - \frac{π}{2} § (\frac{2}{π} x)

Add a constant to the solution

= x sin (x) - \frac{π}{2} § (\frac{2}{π} x) + C

f (x) = (9 - x^{3})^{- 2}

10 y^{^{''}} + 2 y^{^{'}} + 5 y = 0

\frac{d y}{d x} = \frac{4 y}{x}

ln (x + 4)

(x y - y^{2}) d x + x^{3} d y = 0

What is the integral of cos(x)sqrt(x) ?
The integral of cos(x)sqrt(x) is sqrt(x)sin(x)-sqrt(pi/2)\S(sqrt(2/pi)sqrt(x))+C